Neutron Radii of Calcium Isotopes from Pion Total Cross Section Measurements

Abstract

Measurements of the total cross section differences ${\ensuremath{\sigma}}_{T}(^{48}\mathrm{Ca})\ensuremath{-}{\ensuremath{\sigma}}_{T}(^{40}\mathrm{Ca})$ and ${\ensuremath{\sigma}}_{T}(^{44}\mathrm{Ca})\ensuremath{-}{\ensuremath{\sigma}}_{T}(^{40}\mathrm{Ca})$ are reported for positive and negative pions. Optical-model calculations are used to extract values of the rms neutron radius difference for each isotope pair. For $^{48}\mathrm{Ca}$-$^{40}\mathrm{Ca}$ the deduced radius difference agrees with the results of recent $\ensuremath{\alpha}$-particle and proton scattering experiments but is smaller than values predicted from Hartree-Fock calculations.